Lagrange Multiplier

We
introduce a new variable (λ)
called a Lagrange multiplier, and study the Lagrange function defined by

If f(x,y) is a maximum for the original constrained
problem, then there exists λ such that (x,y,λ) is a stationary
point for the Lagrange function (stationary points
are those points where the partial derivatives of Λ are zero). not all stationary points yield a solution of the
original problem.

Thus, the method of
Lagrange multipliers yields a necessary condition
for optimality in constrained problems.

- a powerful tool for solving this class of problems without the need to
explicitly solve the conditions and use them to eliminate extra
variables.